Three-body unitarity with isobars revisited
Abstract
The particle exchange model of hadron interactions can be used to describe three-body scattering under the isobar assumption. Here, we start from the 3->3 scattering amplitude for spinless particles, which contains an isobar-spectator scattering amplitude. Using a Bethe-Salpeter Ansatz for the latter, we derive a relativistic three-dimensional scattering equation that manifestly fulfills three-body unitarity and two-body unitarity for the sub-amplitudes. Furthermore, this property holds for energies above breakup and also in the presence of resonances in the sub-amplitudes.
- Authors:
-
- George Washington Univ., Washington, DC (United States)
- George Washington Univ., Washington, DC (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Indiana Univ., Bloomington, IN (United States). Center for Exploration of Energy and Matter, Physics Dept.
- Publication Date:
- Research Org.:
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP); National Science Foundation (NSF)
- OSTI Identifier:
- 1389749
- Report Number(s):
- JLAB-THY-17-2496; DOE/OR/23177-4206; arXiv:1706.06118
Journal ID: ISSN 1434-6001; PII: 920
- Grant/Contract Number:
- AC05-06OR23177; SC001658; PHY-1452055; 1415459
- Resource Type:
- Accepted Manuscript
- Journal Name:
- European Physical Journal. A
- Additional Journal Information:
- Journal Volume: 53; Journal Issue: 9; Journal ID: ISSN 1434-6001
- Publisher:
- Springer
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Citation Formats
Mai, M., Hu, B., Döring, M., Pilloni, A., and Szczepaniak, A. Three-body unitarity with isobars revisited. United States: N. p., 2017.
Web. doi:10.1140/epja/i2017-12368-4.
Mai, M., Hu, B., Döring, M., Pilloni, A., & Szczepaniak, A. Three-body unitarity with isobars revisited. United States. https://doi.org/10.1140/epja/i2017-12368-4
Mai, M., Hu, B., Döring, M., Pilloni, A., and Szczepaniak, A. Fri .
"Three-body unitarity with isobars revisited". United States. https://doi.org/10.1140/epja/i2017-12368-4. https://www.osti.gov/servlets/purl/1389749.
@article{osti_1389749,
title = {Three-body unitarity with isobars revisited},
author = {Mai, M. and Hu, B. and Döring, M. and Pilloni, A. and Szczepaniak, A.},
abstractNote = {The particle exchange model of hadron interactions can be used to describe three-body scattering under the isobar assumption. Here, we start from the 3->3 scattering amplitude for spinless particles, which contains an isobar-spectator scattering amplitude. Using a Bethe-Salpeter Ansatz for the latter, we derive a relativistic three-dimensional scattering equation that manifestly fulfills three-body unitarity and two-body unitarity for the sub-amplitudes. Furthermore, this property holds for energies above breakup and also in the presence of resonances in the sub-amplitudes.},
doi = {10.1140/epja/i2017-12368-4},
journal = {European Physical Journal. A},
number = 9,
volume = 53,
place = {United States},
year = {2017},
month = {9}
}
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Works referenced in this record:
Hadron Spectroscopy with CLAS and CLAS12
journal, January 2015
- Glazier, D. I.
- Acta Physica Polonica B Proceedings Supplement, Vol. 8, Issue 2
Three-body final state interaction in η→ 3π updated
journal, August 2017
- Guo, P.; Danilkin, I. V.; Fernández-Ramírez, C.
- Physics Letters B, Vol. 771
Spectrum of Three-Body Bound States in a Finite Volume
journal, March 2015
- Meißner, Ulf-G.; Ríos, Guillermo; Rusetsky, Akaki
- Physical Review Letters, Vol. 114, Issue 9
Relativistic Three-Body Theory with Applications to Scattering
journal, October 1968
- Aaron, R.; Amado, R. D.; Young, J. E.
- Physical Review, Vol. 174, Issue 5
Coupled-channel analysis of decay
journal, January 2016
- Nakamura, Satoshi X.
- Physical Review D, Vol. 93, Issue 1
A three-body calculation of πd scattering
journal, March 1976
- Thomas, A. W.
- Nuclear Physics A, Vol. 258, Issue 3
Relating the finite-volume spectrum and the two-and-three-particle matrix for relativistic systems of identical scalar particles
journal, April 2017
- Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.
- Physical Review D, Vol. 95, Issue 7
Analysis of Three-Hadron Final States
journal, October 1973
- Aaron, R.; Amado, R. D.
- Physical Review Letters, Vol. 31, Issue 18
Binding energy of the at unphysical pion masses
journal, December 2015
- Baru, V.; Epelbaum, E.; Filin, A. A.
- Physical Review D, Vol. 92, Issue 11
Dispersion-theoretical analysis of the D + → K − π + π + Dalitz plot
journal, October 2015
- Niecknig, Franz; Kubis, Bastian
- Journal of High Energy Physics, Vol. 2015, Issue 10
Unitarity effects in pion-production isobar amplitudes
journal, October 1975
- Aaron, Ronald; Thompson, Richard H.; Amado, Ralph D.
- Physical Review D, Vol. 12, Issue 7
The COMPASS experiment at CERN
journal, July 2007
- Abbon, P.; Albrecht, E.; Alexakhin, V. Yu.
- Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 577, Issue 3
E (1420) meson as a KK¯ π molecule
journal, August 1990
- Longacre, R. S.
- Physical Review D, Vol. 42, Issue 3
Analytic properties of the scattering amplitude and resonances parameters in a meson exchange model
journal, October 2009
- Döring, M.; Hanhart, C.; Huang, F.
- Nuclear Physics A, Vol. 829, Issue 3-4
Relativistic, model-independent, three-particle quantization condition
journal, December 2014
- Hansen, Maxwell T.; Sharpe, Stephen R.
- Physical Review D, Vol. 90, Issue 11
Three particles in a finite volume
journal, May 2012
- Polejaeva, K.; Rusetsky, A.
- The European Physical Journal A, Vol. 48, Issue 5
Nucleon resonances within a dynamical coupled-channels model of and reactions
journal, September 2013
- Kamano, H.; Nakamura, S. X.; Lee, T. -S. H.
- Physical Review C, Vol. 88, Issue 3
and transition form factors in dispersion theory
journal, September 2012
- Schneider, Sebastian P.; Kubis, Bastian; Niecknig, Franz
- Physical Review D, Vol. 86, Issue 5
Heavy-quark QCD exotica
journal, March 2017
- Lebed, Richard F.; Mitchell, Ryan E.; Swanson, Eric S.
- Progress in Particle and Nuclear Physics, Vol. 93
Recoil corrections in antikaon-deuteron scattering
journal, March 2015
- Mai, Maxim; Baru, Vadim; Epelbaum, Evgeny
- Physical Review D, Vol. 91, Issue 5
Unitary coupled-channels model for three-mesons decays of heavy mesons
journal, December 2011
- Kamano, H.; Nakamura, S. X.; Lee, T. -S. H.
- Physical Review D, Vol. 84, Issue 11
Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
journal, December 2015
- Hansen, Maxwell T.; Sharpe, Stephen R.
- Physical Review D, Vol. 92, Issue 11
Minimal three-body equations with finite-range effects
journal, October 1975
- Amado, R. D.
- Physical Review C, Vol. 12, Issue 4
Towards three-body unitarity in
journal, November 2011
- Magalhães, P. C.; Robilotta, M. R.; Guimarães, K. S. F. F.
- Physical Review D, Vol. 84, Issue 9
Minimal Three-Body Scattering Theory
journal, July 1974
- Amado, R. D.
- Physical Review Letters, Vol. 33, Issue 5
Coupled-channel dynamics in the reactions πN → πN, ηN, KΛ, KΣ
journal, April 2013
- Rönchen, D.; Döring, M.; Huang, F.
- The European Physical Journal A, Vol. 49, Issue 4
The optical potential on the lattice
journal, June 2016
- Agadjanov, Dimitri; Döring, Michael; Mai, Maxim
- Journal of High Energy Physics, Vol. 2016, Issue 6
Dispersive analysis of ω→3π and ϕ→3π decays
journal, May 2012
- Niecknig, Franz; Kubis, Bastian; Schneider, Sebastian P.
- The European Physical Journal C, Vol. 72, Issue 5
Three-body resonances in two-meson–one-baryon systems
journal, April 2008
- Martínez Torres, A.; Khemchandani, K. P.; Oset, E.
- Physical Review C, Vol. 77, Issue 4
Nature of the
journal, May 2015
- Mikhasenko, M.; Ketzer, B.; Sarantsev, A.
- Physical Review D, Vol. 91, Issue 9
Three-body dynamics for the
journal, October 2011
- Baru, V.; Filin, A. A.; Hanhart, C.
- Physical Review D, Vol. 84, Issue 7
Relevance of complex branch points for partial wave analysis
journal, July 2011
- Ceci, S.; Döring, M.; Hanhart, C.
- Physical Review C, Vol. 84, Issue 1
Unitary analytic isobar model for the reaction nucleon-meson to nucleon-meson-meson
journal, June 1978
- Aitchison, I. J. R.; Brehm, J. J.
- Physical Review D, Vol. 17, Issue 11
Theoretical support for the and the recently claimed as molecular resonances
journal, October 2011
- Martínez Torres, A.; Khemchandani, K. P.; Jido, D.
- Physical Review D, Vol. 84, Issue 7
Dispersion relations for $$\eta '\rightarrow \eta \pi \pi $$ η ′ → η π π
journal, July 2017
- Isken, Tobias; Kubis, Bastian; Schneider, Sebastian P.
- The European Physical Journal C, Vol. 77, Issue 7
Pion-Pion Scattering and Decay
journal, August 1960
- Khuri, N. N.; Treiman, S. B.
- Physical Review, Vol. 119, Issue 3
Scattering of unstable particles in a finite volume: The case of scattering and the resonance
journal, March 2012
- Roca, L.; Oset, E.
- Physical Review D, Vol. 85, Issue 5
Three - Meson Resonances in a Relativistic Faddeev - Type Approach
journal, September 1972
- Mennessier, G.; Pasquier, J. -Y.; Pasquier, R.
- Physical Review D, Vol. 6, Issue 5
Dynamical coupled-channels model of reactions: Determination of partial-wave amplitudes
journal, December 2014
- Kamano, H.; Nakamura, S. X.; Lee, T. -S. H.
- Physical Review C, Vol. 90, Issue 6
Eta photoproduction in a combined analysis of pion- and photon-induced reactions
journal, June 2015
- Rönchen, D.; Döring, M.; Haberzettl, H.
- The European Physical Journal A, Vol. 51, Issue 6
Faddeev-chiral unitary approach to the scattering length
journal, March 2013
- Mizutani, T.; Fayard, C.; Saghai, B.
- Physical Review C, Vol. 87, Issue 3
Dispersive approaches for three-particle final state interaction
journal, October 2015
- Guo, Peng; Danilkin, I. V.; Szczepaniak, Adam P.
- The European Physical Journal A, Vol. 51, Issue 10
Isobar formalism and one-pion-exchange partial-wave cross sections in
journal, July 1977
- Aaron, Ronald; Amado, R. D.; Arndt, Richard A.
- Physical Review D, Vol. 16, Issue 1
Dispersive analysis of
journal, May 2015
- Danilkin, I. V.; Fernández-Ramírez, C.; Guo, P.
- Physical Review D, Vol. 91, Issue 9
Remarks on study of from effective field theory with pion-exchange interaction
journal, February 2015
- Baru, V.; Epelbaum, E.; Filin, A. A.
- Physical Review D, Vol. 91, Issue 3
New approach to the theory of coupled πNN-NN systems
journal, April 1980
- Avishai, Y.; Mizutani, T.
- Nuclear Physics A, Vol. 338, Issue 2
Relativistic isobar model: Spinless particles
journal, May 1976
- Aaron, R.; Amado, R. D.
- Physical Review D, Vol. 13, Issue 9
Hadron Spectroscopy at BESIII
journal, April 2016
- Fang, Shuangshi
- Nuclear and Particle Physics Proceedings, Vol. 273-275
Reduction of the three-particle collision problem to multi-channel two-particle Lippmann-Schwinger equations
journal, June 1967
- Alt, E. O.; Grassberger, P.; Sandhas, W.
- Nuclear Physics B, Vol. 2, Issue 2
The Physics of the B Factories
journal, November 2014
- Bevan, A. J.; Golob, B.; Mannel, Th.
- The European Physical Journal C, Vol. 74, Issue 11
Multiquark resonances
journal, January 2017
- Esposito, A.; Pilloni, A.; Polosa, A. D.
- Physics Reports, Vol. 668
Three-body final state interaction in
journal, September 2015
- Guo, Peng; Danilkin, Igor V.; Schott, Diane
- Physical Review D, Vol. 92, Issue 5
Linear Integral Equations for Relativistic Multichannel Scattering
journal, February 1966
- Blankenbecler, R.; Sugar, R.
- Physical Review, Vol. 142, Issue 4
Unified theory of γN→πN , ππN , and πN→πN , ππN reactions
journal, October 1988
- Afnan, I. R.
- Physical Review C, Vol. 38, Issue 4
Three-particle quantization condition in a finite volume: 2. General formalism and the analysis of data
journal, October 2017
- Hammer, Hans-Werner; Pang, Jin-Yi; Rusetsky, Akaki
- Journal of High Energy Physics, Vol. 2017, Issue 10, 31 p.
New approach to the theory of coupled πNN-NN systems
journal, February 1981
- Avishai, Y.; Mizutani, T.
- Nuclear Physics A, Vol. 352, Issue 3
The Compass Experiment at CERN
conference, January 2005
- Magnon, A.
- STRUCTURE OF THE NUCLEON AT LARGE BJORKEN x: 2nd International Workshop on the Structure of the Nucleon at Large Bjorken x; HiX2004, AIP Conference Proceedings
Three particles in a finite volume
conference, October 2012
- Polejaeva, Kathryn; Rusetsky, Akaki
- Proceedings of Sixth International Conference on Quarks and Nuclear Physics — PoS(QNP2012)
Recoil corrections in antikaon-deuteron scattering
conference, June 2016
- Mai, Maxim; Baru, Vadim; Epelbaum, Evgeny
- Proceedings of The 8th International Workshop on Chiral Dynamics — PoS(CD15)
The Physics of the B Factories
text, January 2014
- Bevan, A. J.; Golob, B.; Mannel, Th.
- Universität Regensburg
The COMPASS experiment at CERN
conference, January 1997
- Bravar, Alessandro
- The 5th international workshop on deep inelastic scattering and QCD, AIP Conference Proceedings
Hadron Spectroscopy at BESIII
journal, December 2018
- Albrecht, Malte
- Journal of Physics: Conference Series, Vol. 1137
The Physics of the B Factories
text, January 2014
- Bevan, A. J.; Golob, B.; Mannel, Thomas
- RWTH Aachen University
New approach to the theory of coupled πNN-NN systems
journal, September 1979
- Avishai, Y.; Mizutani, T.
- Nuclear Physics A, Vol. 326, Issue 2-3
Recoil corrections in antikaon-deuteron scattering
journal, January 2016
- Mai, Maxim; Baru, Vadim; Epelbaum, Evgeny
- EPJ Web of Conferences, Vol. 113
Hadron Spectroscopy at BESIII
journal, January 2016
- Destefanis, Marco
- EPJ Web of Conferences, Vol. 129
Unitary coupled-channels model for three-mesons decays of heavy mesons
text, January 2011
- Kamano, H.; Nakamura, S. X.; Lee, T. -S. H.
- arXiv
Faddeev-Chiral Unitary Approach to the $K^- d$ scattering length
text, January 2012
- Mizutani, T.; Fayard, C.; Saghai, B.
- arXiv
Dynamical coupled-channels model of $K^- p$ reactions (I): Determination of partial-wave amplitudes
text, January 2014
- Kamano, H.; Nakamura, S. X.; Lee, T. -S. H.
- arXiv
A relativistic, model-independent, three-particle quantization condition
text, January 2014
- Hansen, Maxwell T.; Sharpe, Stephen R.
- arXiv
Recoil corrections in antikaon-deuteron scattering
text, January 2014
- Mai, Maxim; Baru, Vadim; Epelbaum, Evgeny
- arXiv
Eta photoproduction in a combined analysis of pion- and photon-induced reactions
text, January 2015
- Rönchen, D.; Döring, M.; Haberzettl, H.
- arXiv
Expressing the three-particle finite-volume spectrum in terms of the three-to-three scattering amplitude
text, January 2015
- Hansen, Maxwell T.; Sharpe, Stephen R.
- arXiv
Heavy-Quark QCD Exotica
text, January 2016
- Lebed, Richard F.; Mitchell, Ryan E.; Swanson, Eric S.
- arXiv
Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles
text, January 2017
- Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.
- arXiv
Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
text, January 2017
- Hammer, H. -W.; Pang, J. -Y.; Rusetsky, A.
- arXiv
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journal, August 2019
- Mikhasenko, M.; Wunderlich, Y.; Jackura, A.
- Journal of High Energy Physics, Vol. 2019, Issue 8
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journal, October 2017
- Hammer, Hans-Werner; Pang, Jin-Yi; Rusetsky, Akaki
- Journal of High Energy Physics, Vol. 2017, Issue 10, 31 p.
Developments of the Jülich–Bonn Dynamical Coupled-Channel Analysis
journal, October 2018
- Döring, M.
- Few-Body Systems, Vol. 59, Issue 6
Nucleon form factors in dispersively improved chiral effective field theory. II. Electromagnetic form factors
journal, May 2018
- Alarcón, J. M.; Weiss, C.
- Physical Review C, Vol. 97, Issue 5
Equivalence of three-particle scattering formalisms
journal, August 2019
- Jackura, A. W.; Dawid, S. M.; Fernández-Ramírez, C.
- Physical Review D, Vol. 100, Issue 3
Pion scattering in the isospin channel from elongated lattices
journal, August 2019
- Culver, C.; Mai, M.; Alexandru, A.
- Physical Review D, Vol. 100, Issue 3
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journal, September 2019
- Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.
- Physical Review D, Vol. 100, Issue 5
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journal, March 2020
- Mai, M.; Döring, M.; Culver, C.
- Physical Review D, Vol. 101, Issue 5
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journal, June 2018
- Döring, M.; Hammer, H. -W.; Mai, M.
- Physical Review D, Vol. 97, Issue 11
Numerical study of the relativistic three-body quantization condition in the isotropic approximation
journal, July 2018
- Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.
- Physical Review D, Vol. 98, Issue 1
Variational approach to -body interactions in finite volume
journal, November 2018
- Guo, Peng; Döring, Michael; Szczepaniak, Adam P.
- Physical Review D, Vol. 98, Issue 9
Pole position of the from -decay
journal, November 2018
- Mikhasenko, M.; Pilloni, A.; Jackura, A.
- Physical Review D, Vol. 98, Issue 9
Three-particle systems with resonant subprocesses in a finite volume
journal, January 2019
- Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.
- Physical Review D, Vol. 99, Issue 1
Towards the minimal spectrum of excited baryons
journal, January 2019
- Landay, J.; Mai, M.; Döring, M.
- Physical Review D, Vol. 99, Issue 1
Finite-Volume Spectrum of and Systems
journal, February 2019
- Mai, M.; Döring, M.
- Physical Review Letters, Vol. 122, Issue 6
Three-body unitarity in the finite volume
journal, December 2017
- Mai, M.; Döring, M.
- The European Physical Journal A, Vol. 53, Issue 12
The impact of $K^{+}\Lambda$ K + Λ photoproduction on the resonance spectrum
journal, June 2018
- Rönchen, D.; Döring, M.; Meißner, U. -G.
- The European Physical Journal A, Vol. 54, Issue 6
Phenomenology of relativistic $$\mathbf {3}\rightarrow \mathbf {3}$$ 3 → 3 reaction amplitudes within the isobar approximation
journal, January 2019
- Jackura, A.; Fernández-Ramírez, C.; Mathieu, V.
- The European Physical Journal C, Vol. 79, Issue 1
Three-body spectrum in a finite volume: the role of cubic symmetry
text, January 2018
- Döring, M.; Hammer, H. -W.; Mai, M.
- GSI Helmholtzzentrum fuer Schwerionenforschung, GSI, Darmstadt
Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
text, January 2017
- Hammer, H. -W.; Pang, J. -Y.; Rusetsky, A.
- arXiv
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text, January 2017
- Alarcón, J. M.; Weiss, C.
- arXiv
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text, January 2018
- Döring, M.; Hammer, H. -W.; Mai, M.
- arXiv
Numerical study of the relativistic three-body quantization condition in the isotropic approximation
text, January 2018
- Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.
- arXiv
Variational approach to $N$-body interactions in finite volume
text, January 2018
- Guo, Peng; Döring, Michael; Szczepaniak, Adam P.
- arXiv
Three-particle systems with resonant subprocesses in a finite volume
text, January 2018
- Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.
- arXiv
Three-body scattering: Ladders and Resonances
text, January 2019
- Mikhasenko, M.; Wunderlich, Y.; Jackura, A.
- arXiv
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text, January 2019
- Mai, M.; Döring, M.; Culver, C.
- arXiv